Américo López | Universidade de São Paulo (original) (raw)

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Papers by Américo López

Research paper thumbnail of Interval exchange transformations and foliations on infinite genus 2-manifolds

Ergodic Theory and Dynamical Systems, 2004

For each of the following properties, there is an isometric generalized interval exchange transfo... more For each of the following properties, there is an isometric generalized interval exchange transformation (i.e. isometric GIET) having such property: (a) non-trivial recurrence orbits are exceptional and the union of them is a dense set, moreover the intersection of the closure of two such orbits is the union of finite orbits; (b) coexistence of dense orbits and exceptional orbits; (c) existence of a dense sequence of exceptional orbits mathcalO(pk)colonk=1,2,dotsc\{\mathcal{O}(p_k)\colon k=1,2,\dotsc\}mathcalO(pk)colonk=1,2,dotsc such that overlinemathcalO(p1)subsetneqqoverlinemathcalO(p2)subsetneqqdotsbsubsetneqqoverlinemathcalO(p_k)subsetneqqdotsb\overline{\mathcal{O}(p_1)}\subsetneqq\overline{\mathcal{O}(p_2)}\subsetneqq\dotsb\subsetneqq\overline{\mathcal{O}(p_k)}\subsetneqq\dotsboverlinemathcalO(p_1)subsetneqqoverlinemathcalO(p2)subsetneqqdotsbsubsetneqqoverlinemathcalO(pk)subsetneqqdotsb. Moreover, the isometric GIET can be suspended to a smooth foliation, without singularities, on a 2-manifold. The exceptional (respectively dense) orbits of the GIET give rise to exceptional (respectively dense) leaves of the foliation. Finite genus 2-manifolds cannot support orientable foliations with the considered dynamics.

Research paper thumbnail of Affine interval exchange transformation without an isometric model

Bulletin of the Brazilian Mathematical Society, New Series, 2007

Contrary to the case of interval exchange transformation, we show that generalized affine interva... more Contrary to the case of interval exchange transformation, we show that generalized affine interval exchange transformation (affine GIET), with or without flips and admitting dense orbits, may not be conjugated to an isometric GIET. This result is proved by constructing explicitly one such affine GIET.

Research paper thumbnail of A structure theorem for foliations on non-compact 2-manifolds

Ergodic Theory and Dynamical Systems - ERGOD THEOR DYN SYST, 2005

We consider singular orientable foliations, which admit nontrivial recurrent leaves, on two-manif... more We consider singular orientable foliations, which admit nontrivial recurrent leaves, on two-manifolds of finite or infinite genus. We give a structure theorem for this foliations. This one is similar to Gutierrez's structure theorem [Gu1] for flows on compact surfaces. May, 2002 ICMC-USP

Research paper thumbnail of Interval exchange transformations and foliations on infinite genus 2-manifolds

Ergodic Theory and Dynamical Systems, 2004

Research paper thumbnail of Interval exchange transformations and foliations on infinite genus 2-manifolds

Ergodic Theory and Dynamical Systems, 2004

For each of the following properties, there is an isometric generalized interval exchange transfo... more For each of the following properties, there is an isometric generalized interval exchange transformation (i.e. isometric GIET) having such property: (a) non-trivial recurrence orbits are exceptional and the union of them is a dense set, moreover the intersection of the closure of two such orbits is the union of finite orbits; (b) coexistence of dense orbits and exceptional orbits; (c) existence of a dense sequence of exceptional orbits mathcalO(pk)colonk=1,2,dotsc\{\mathcal{O}(p_k)\colon k=1,2,\dotsc\}mathcalO(pk)colonk=1,2,dotsc such that overlinemathcalO(p1)subsetneqqoverlinemathcalO(p2)subsetneqqdotsbsubsetneqqoverlinemathcalO(p_k)subsetneqqdotsb\overline{\mathcal{O}(p_1)}\subsetneqq\overline{\mathcal{O}(p_2)}\subsetneqq\dotsb\subsetneqq\overline{\mathcal{O}(p_k)}\subsetneqq\dotsboverlinemathcalO(p_1)subsetneqqoverlinemathcalO(p2)subsetneqqdotsbsubsetneqqoverlinemathcalO(pk)subsetneqqdotsb. Moreover, the isometric GIET can be suspended to a smooth foliation, without singularities, on a 2-manifold. The exceptional (respectively dense) orbits of the GIET give rise to exceptional (respectively dense) leaves of the foliation. Finite genus 2-manifolds cannot support orientable foliations with the considered dynamics.

Research paper thumbnail of Affine interval exchange transformation without an isometric model

Bulletin of the Brazilian Mathematical Society, New Series, 2007

Contrary to the case of interval exchange transformation, we show that generalized affine interva... more Contrary to the case of interval exchange transformation, we show that generalized affine interval exchange transformation (affine GIET), with or without flips and admitting dense orbits, may not be conjugated to an isometric GIET. This result is proved by constructing explicitly one such affine GIET.

Research paper thumbnail of A structure theorem for foliations on non-compact 2-manifolds

Ergodic Theory and Dynamical Systems - ERGOD THEOR DYN SYST, 2005

We consider singular orientable foliations, which admit nontrivial recurrent leaves, on two-manif... more We consider singular orientable foliations, which admit nontrivial recurrent leaves, on two-manifolds of finite or infinite genus. We give a structure theorem for this foliations. This one is similar to Gutierrez's structure theorem [Gu1] for flows on compact surfaces. May, 2002 ICMC-USP

Research paper thumbnail of Interval exchange transformations and foliations on infinite genus 2-manifolds

Ergodic Theory and Dynamical Systems, 2004

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